Hawking: No 'Theory of Everything'

Flash Modin writes "In a Scientific American essay based on their new book A Grand Design, Stephen Hawking and Leonard Mlodinow are now claiming physicists may never find a theory of everything. Instead, they propose a 'family of interconnected theories' might emerge, with each describing a certain reality under specific conditions. The claim is a reversal for Hawking, who claimed in 1980 that there would be a unified theory by the turn of the century."

Comments

The hand of Godel?

[Hatta]

Godel proved that all formal systems are either incomplete or inconsistent. Perhaps that's what we're dealing with here.

Re:The hand of Godel?

[abigor]

Godel used the term "formal system" to specifically mean a recursive axiomatic system that can do arithmetic. I don't think it really applies here.

Re:The hand of Godel?

[w0mprat]

We work on the assumption that the laws of physics are perfect and complete, and we are just trying to reveal them. The laws of physics could work well enough but actually be incomplete and consistent as you point out. They could even bebe crappy, bloated and buggy with lots of missing chunks, unused bloat and even errors.

If the laws of physics emerged naturally, for example budding off from a parent universe, and subject to a process of evolution I would expect theories of everything to be 'just good enough' and barely work rather than somehow perfect and elegant and mystical. Much like the junk DNA, apendix and mens nipples that rides along with us because evolution didn't really have pressure need to get rid of them.

I would say we should by default expect a theory of everything a whole basket of seemingly clumsy unweildy theories that barely fit together - after all they only need to be just good enough for us to be here and not any better. If we expect flawless elegant unified symmetry and beauty, then we'd need to demonstrate why (without invoking God to explain etc).

Researchers have been seduced by subjectively elegant and simple equations all the way back to F=MA ... these worked well enough, but were ultimately wrong, the truth was more complex and nuanced, but now we're finding the universe is fuzzy, clumsy and possibly buggy (inflation, possible variations in c, other weirdness).

Re:The hand of Godel?

[Hatta]

Aren't the laws of physics axioms for the universe? Isn't the idea behind a grand unified theory to find one or two simple mathematical expressions (axioms) from which the rest of the universe can be derived? The universe is clearly Turing complete, so I really don't see how it wouldn't apply.

Re:The hand of Godel?

[Abcd1234]

Because you don't understand Godel's theorem, which is grossly misunderstood by basically everyone who's ever heard of it colloquially. Here, have a little read on how it's so wonderfully misunderstood, and so horribly misapplied.

Re:The hand of Godel?

[luis_a_espinal]

Prove it.

Easy. Proof by contradiction:

Assume there is a universal (and extremely long) string U that encodes a countable set containing all problems P_i (encoded as decision problems) that are possible in this Universe. We can trivially see that indeed U must contain all problems that exist for it to represent the Universe. Otherwise, it does not represent the Universe.

Furthermore, if every decision problem P_i in U is decidable, then there is a (not necessarily unique) Turing Machine T_i that halts in finite time for each problem P_i in U. With this assumption, then there would be a Universal Turing Machine T that is a chain of all turning machines T_i that can compute (and thus give meaning) to all problems P_i in U (the string encoding of the universe.) That is, T is the universe.

But the halting problem is not in U. In fact, U cannot contain neither semi decidable nor undecidable problems (which was our base assumption). However, the halting problem (and all other semi-decidable and undecidable problems) exists in the Universe. U then, cannot be an encoding of the universe, and T (a turing machine) cannot be the Universe either.

qed.

It may just be a matter of scale - we simply aren't able to take a large enough view. A turing machine, if you only look at one small part of it, is no longer turing-complete. And the presence of a turing-complete machine doesn't mean the enclosing reality suddenly is turing-complete. Think babushka dolls, as in Soviet Russia, Turing completes YOU!

Dude, the fact that there are problems in this Universe (and thus part of it) that are not turing computable (a mathematical fact indeed) does indicate that the universe is not a Turing complete nor Turing computable. The universe is naturally uncountable.

Re:The hand of Godel?

[tomhudson]

First problem ( of many ) - a representation of something is not that something. This is something that programmers forget all the time. There is no such thing as objects, methods, function calls, etc. Those are just representations. At a higher level, ordering a pizza online, and them sending you a fax of that pizza, is not going to work either. Even them sending you a complete description of the state of every single atom in a pizza is not going to work. Information, contrary to popular belief, is not equivalent to the thing being described.

In other words, even if you had a machine that was able to represent every single state of the universe, it is not equivalent to the universe. Any description of something, no matter how detailed, is not that thing, no matter how many times people chant "information theory says otherwise." It's like the pastor who preaches against same-sex marriage, saying it's unnatural and that same-sex behaviour doesn't occur in nature, but completely ignores the male dog humping his leg.

However, what you offer is not proof by contradiction. It buys into the idea that there's the possibility that the universe might be represented by a Turing machine. That's the flawed premise (but try to get people to see it when they've got their precious theories on the line).

Also, the halting problem is trivially solved by allowing the arrow of time to reverse at the end of each calculation (say once a second), so that even a near-infinite solution must, by definition, complete in 1 second of "real" time. In other words, either the Turing machine continues to exist after one second, or it disappears - stuck in an infinite time loop. This lets you know that the problem is either solvable, or not.

As for the "dude" bit, please see my profile thx bye!

Re:The hand of Godel?

[John Hasler]

The universe contains complete, formal, logical systems (e.g. computers).

Real computers are not complete, formal, logical systems.

Are they not governed by the laws of physics?

Real computers are, yes. And they are, therefor, not complete, formal, logical systems. The future state of a real computer is not entirely determined by its current state.

Re:The hand of Godel?

[Goldsmith]

I don't know Godel as well as some other people here, but I do know physics and you're making a lot of assumptions there, starting with that the universe can be "derived" from a theory of everything. The name is a little unfortunate, but the goal of a theory of everything is to create a unified description of the fundamental forces, not a program to simulate the entire universe. If you wanted to simply say "the theory of everything won't be able to tell you absolutely everything about every particle in the universe," you'd be right, and probably that's where you're going with your incompleteness thing.

More fundamentally though, you're assuming the universe is a logical system. From a physicists point of view, it is a happy coincidence that rigorous mathematics is useful in describing the universe, but there is nothing that demands that this is the case (more practically: we're happy in physics to have assumptions about things like causality and time invariance, where needed).

This may sound crazy to most people, but why exactly mathematics has been so successful in physics is still a subject of debate among physicists: whether mathematics approximates an ultimately imperfect physical reality or mathematics *is* physical reality. I don't think it will be settled soon.

Re:The hand of Godel?

[PenguiN42]

However, the halting problem (and all other semi-decidable and undecidable problems) exists in the Universe.

This is a HUGE assumption on which your entire argument hinges, so I think you need to define it more precisely, and provide some evidence that it is true.

Your argument seems to fall apart due to equivocation -- at the beginning you define a set of "problems" that the universe turing machine has to solve. For example, one of those "problems" might be "if you arrange mass in a certain configuration, in which direction will it accelerate?"

However, you then include "the halting problem" in this set. Bzzzt, full stop. This is a decidedly different sense of the word "problem." In this case, we're talking about an abstract idea that only exists as definitions on paper and in peoples' minds, but doesn't actually physically exist in the universe. In other words, our universe can talk about and consider and represent undecidable problems, but that doesn't mean it can actually solve them.

If you disagree, please describe a phyisical system that is "the halting problem" or some other undecidable problem and show that the universe can indeed resolve it.

Oblig

[gmuslera]

xkcd

Re:Oblig

[blair1q]

You know, it's no longer necessary to actually link to xkcd from /.

Just mention the number.

We'll laugh just as hard.

Re:Oblig

[jewens]

Some people just don't know how to tell a joke.

Re:Oblig

[EnsilZah]

It got me to check 404 though, which actually displays a 404, given 403 and 405 do point to actual comics leads me to believe is actually intentional, geeze this guy is committed.

unified theory by the turn of the century

[Culture20]

"The claim is a reversal for Hawking, who claimed in 1980 that there would be a unified theory by the turn of the century."

I think the turn of the century reversed his claim for him.

Re:Celebrity physicist troll train

[Sonny Yatsen]

He's a theoretical physicist. Theories ARE his results.

Re:Celebrity physicist troll train

[Anonymous Coward]

What sort of people do you think predict the as yet unobserved particles that Fermi and LHC people are looking for? Though I doubt Hawking is right on this one, not many besides you would say he was on the sidelines anyway.

Past His Prime

[Wannabe Code Monkey]

I certainly hate to say it. And I certainly don't think I'm any smarter. But, Hawking is past his prime. It seems like he's been saying stuff recently just to say stuff. Maybe it's for attention, maybe it's because he knows extraordinary claims will sell headlines and his books/documentaries, or maybe it's because he actually believes in them. However, after his comments on active SETI being dangerous and now this... I don't know, it's like watching an amazing baseball player, past his prime, coaching a crappy minor league team. It's hard to criticize because I was never as good as he, and even now I couldn't manage a Denny's, but I don't really want to watch him either.

Re:Past His Prime

[amicusNYCL]

It seems like he's been saying stuff recently just to say stuff.

Totally. He just likes to hear his own voice.

Re:Past His Prime

[Wannabe Code Monkey]

Totally. He just likes to hear his own voice.

Now you're making me wish that I hadn't commented in this discussion just so I could mod you up. Although if I had never commented, then you wouldn't have been able to reply to me and I wouldn't have been able to mod you up anyway. Maybe some smart scientist could help us out with this paradox.

Re:Past His Prime

[interkin3tic]

It happens. James Watson, who was part of the team that discovered the structure of DNA, has been saying crazier things for years.

My favorite was his presentation on why men liked butts. Certainly funnier than his comments on race.

Scientists sometimes don't age well. We probably age better on average than rock stars, but then again people pay don't take what rock stars say as seriously as scientists.

Re:Past His Prime

[deodiaus2]

The comment about Hawkins being past his prime is really ugly, especially coming from you. I think Hawkins is honest enough to say that he does not know or understand something if he doesn't. Hawkins refered to himself as being lazy in his early years in college, so he does admit some of his shortcomings. Ronnie Reagan was often ignorant of the facts, but he said them with such conviction that even people who knew had to go back to check their references before retorting. We survived Ronnie, so I'm more inclined to trust Hawkins.
It might be that it takes a lifetime to learn enough physics in order to make a statement like that. Also, as someone said, the theory of everything might fall into Godel's incompleteness type of problem. Quantum physics is a patchwork of knowledge without enough theory to explain itself. Or the theory could be beyond Human understanding.

Re:Past His Prime

[smooth wombat]

Just invent a one-way time machine. Then you could mate with all the women you wanted when men become scarce (after the giraffes have long since ceased to rule the planet) then move forward in time, wait for the last photon to decay, see the Big Bang take place, take a potshot at Hitler and as the current time approaches, slow down enough to see the comments appearing, wait for someone else to make the joke then mod them up!

Of course you have to hope this universe isn't 10' higher than the previous universe.

Re:Past His Prime

[mcgrew]

But, Hawking is past his prime.

He's only ten years older than me, kid. He's a physicist, not a football player. Unless you get alzheimer's or drink a lot or play high impact sports (boxing or non-US football) your brain doesn't suffer much if any.

Like one of my old college profs was fond of saying, "kid, I've forgotten more than you've ever learned".

However, after his comments on active SETI being dangerous

I agree with him about that. Actively hunting for species that make us look like chimpanzes by comparison doesn't seem like the smartest thing we can do.

coaching a crappy minor league team

I'd say that research at Cambrige is hardly equivalent to coaching a crappy minor league team. And the list of his accomplishments puts your "past his prime" into perspective (see the wikipedia article on him):

1975 Eddington Medal
1976 Hughes Medal of the Royal Society
1979 Albert Einstein Medal
1981 Franklin Medal
1982 Order of the British Empire (Commander)
1985 Gold Medal of the Royal Astronomical Society
1986 Member of the Pontifical Academy of Sciences
1988 Wolf Prize in Physics
1989 Prince of Asturias Awards in Concord
1989 Companion of Honour
1999 Julius Edgar Lilienfeld Prize of the American Physical Society[45]
2003 Michelson Morley Award of Case Western Reserve University
2006 Copley Medal of the Royal Society[46]
2008 Fonseca Price of the University of Santiago de Compostela[47]
2009 Presidential Medal of Freedom, the highest civilian honour in the United States[4]

"When I hear of Schrödinger's cat, I reach for my pistol." -- Stephen Hawking

I think I'll change my sig...

Re:Past His Prime

[oldhack]

You're conflating blings with accomplishment. Should have listed his papers instead of awards given to him.

Wisdom from DS9

[MBGMorden]

I'm reminded of a scene from DS9. Sure it's fiction, but it always held some sway with me:

Bashir: "Trevean was right. There is no cure. The Dominion made sure of that. But I was so arrogant, I thought I could find one in a week!"
Jadzia: "Maybe it was arrogant to think that. But it's even more arrogant to think there isn't a cure just because you couldn't find it."

Hawking a smart guy, but he by no means knows everything. Throwing in the towel and declaring that there is no right answer simply because he hasn't found it just doesn't hold much water with me. We might not figure it out for 100 years. We might figure it out tomorrow. We might NEVER figure it out, but simple logic says that there is a unified equation. It might not be simple or pretty, but if the universe operates on a consistent set of physical laws, it's out there.

Re:Wisdom from DS9

[electron sponge]

"The universe is not required to be in perfect harmony with human ambition." - Carl Sagan

Re:Wisdom from DS9

[guyminuslife]

Simple logic says a lot of things, some of which it turns out are not true.

Re:Wisdom from DS9

[MortimerGraves]

I wonder if it may be an example of Clarke's First Law:

"When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is probably wrong."

Re:Wisdom from DS9

[petermgreen]

Well, that seemed strange to me, so I looked back over the textbook's diagram for a NOR gate. I thought, "Surely this can't be correct. If you switch the pMOS transistors and the nMOS transistors, then you've got a logical AND gate.
Really the important rule is that there has to be voltage in the right direction between gate and source to turn a transistor on. So if you try to use a N channel in the top side of a logic circuit (or a P channel in the bottom side) you will get a follower (output voltage follows input voltage at some offset) rather than a switch.

You can try building it if you want and with the right transistors it will work up to a point but the output levels will always be lower than the input you feed in (unlike with a proper CMOS gate that relies on switch-like behaviour).

Emergence might be infinite...

[RyanFenton]

I don't actually mind if this is the case. What it means then, is that new properties of aggregated matter emerge as you go up, and up in scope and scale, and that there does not have to be a set relationship on what rules must emerge.

Other than aesthetics, those emergent rules don't have to carry a thread of logic visible at all scopes. Rather, you just need to have the large number of interactions actually occur in relationship to eachother to see the combined effect, with many aspects unforeseeable by only observing the elements many magnitudes smaller.

Whether this might make the universe a more or less beautiful puzzle to figure out is open to interpretation.

Ryan Fenton

Excuse me, Dr. Hawking?

[Theory of Everything]

I'm right here. I promise I do exist. Really.

Re:Excuse me, Dr. Hawking?

[neo-mkrey]

I'm torn -- do I give you +1 Funny or +1 Informative?? Ooops, seeing as I have now posted, you will get neither.

Just a result of age

[Troggie87]

As scientists age they become somewhat jaded, it happens to a lot of people. Hawking has seen a problem he thought was about to be solved get ever more complex while little new progress has been made. I don't blame him for changing his stance. I had a professor during my undergrad who had been a part of some of the first fusion research, and he would occasionally bring up that he didn't think it was possible. According to him, "the kids today are trying what we tried and couldn't get to work back then" (Paraphrased). Maybe doubting there is a solution to the problems you have struggled with all your life is the best way to find peace as your life winds down?

Oh, on a personal opinion note, I doubt we will ever find a *provable* theory of everything. Eventually someone will put together something that relates a lot of complex fields, but I suspect it will be something ad hoc and beyond the practical limits of humanity to test. (*cough* string theory variant *cough*)

You forget important addition to Goedel's theorem

[Cyberax]

You forget important addition to Goedel's theorem. Namely: "all philosophical consequences of Godel's theorem are bunk" (including this one).

Regarding your comment: there ARE complete and consistent formal systems. For example, real number theory is complete.

You can't have consistent, complete system if it's _complex_ _enough_ to describe integers.

Re:Celebrity physicist troll train

[guyminuslife]

String Theory says there is.

Re:What kind of semantic bullshit is this?

[onionman]

Instead, they propose a "family of interconnected theories" might emerge

Which, if you read them all at the same sitting and follow all the connections, just might read like one big...unified theory.

This seems very, very close to a distinction without a difference.

No, there is a very important difference. Hawking is stating that there may be "locally everywhere solutions" without a "global solution." This is a very important concept in advanced mathematics. Go read about the mathematical terms "sheaf" and "local-global principle."

Hawking is essentially saying that there very well may not be one single theory which explains everything. Instead, there may be a bunch of theories, each of which is valid only in certain areas, and which agree with one another where they overlap, even without a global solution.

For a simple example which many readers may already be familiar with, consider the complex logarithm (e.g. the natural log on the complex numbers). To make it well defined, you must make a "branch cut" and decide which branch you want to take. Different branches agree where they overlap, but there is no single global solutions... just a patchwork of solutions that agree where needed (blah, blah lift to a covering space). Pick up a book on complex analysis for details.

In other news...

[djupedal]

...Theory of Everything held a press conference today, stating "There is no Stephen Hawking."

When asked what the implications were as to whether or not there could ever be a Stephen Hawking, ToE replied "The door is open for a Stephen Hawking in the future, but it can only be a possibility if graphene birds fly out of my lily white butt..."

Re:Celebrity physicist troll train

[ColdWetDog]

It's about time they rethink this artificial theoretical/experimental barrier if all the "theories" being cooked up are so far out of the realm of verification that they might as well move to philosophy department.

I mean, it wouldn't it be surprising if they were given advanced degrees like "Doctor of Philosophy" or something like that?

What about Dr. Cooper's work?

[JAZ]

I've been watching documentaries about Dr Sheldon Cooper's work out at Caltech and I'm lead to believe that he's very close to proving String Theory as a Grand Unified Theory.

Surely, Professor Hawking is aware of this research?

Clarke said it best

[MpVpRb]

When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong

Feynman agreed...though much earlier

[PerlHeadJax]

From Gleick's "Genius: The Life and Science of Richard Feynman"...

"'People say to me, "Are you looking for the ultimate laws of physics?" No, I'm not...If it turns out there is a simple ultimate law which explains everything, so be it--that would be very nice to discover. If it turns out it's like an onion with millions of layers...then that's the way it is.' He believed that his colleagues were claiming more success at unification than they had achived--that disparate theories had been pasted together tenuously. When Hawking said, 'We may now be near the end of the search for the ultimate laws of nature,' many particle physicists agreed. But Feynman did not. 'I've had a lifetime of that,' he said on another occasion. 'I've had a lifetime of people who believe that the answer is just around the corner.... But again and again it's been a failure. Eddington, who thought that with the theory of electrons and quantum mechanics everything was going to be simple...Einstein, who thought that he had a unified thoeiry just around the corner but didn't know anything about nuclei and was unable of course to guess it...People think the're very close to the answer, but I don't think so....

Whether or not nature has an ultimate, simple, unified, beautiful form is an open question, and I don't want to say either way.'"

(From the epilogue of the book, pp. 432-433, emph. added.)